Leon Clarke put Coventry in front after six minutes of Sunday's League One clash at Sixfields, before Callum Wilson smashed in his 10th of the season moments before the break to make it two.
Clarke added the third after 49 minutes but when substitute Lyle Taylor fired his 62nd-minute free-kick through the wall and into the net, the momentum shifted.
Taylor headed a second 10 minutes from time but City clung on.
Pressley said: "We've now won our past two league games and move on to 10 points, which considering what we have been through, is a remarkable tally at this moment in time.
"But credit to Sheffield United, I think that when you lose a manager you are always going to get a response from a group of players and finding themselves 3-0 down away from home, they had nothing to lose.
"After they got a bit of momentum, we struggled to find our rhythm again and our passing again but saying that we had a couple of really good chances to kill the game off.
"It's another terrific result for us - but you certainly get your money's worth here, 29 goals in six games.
"The front two's combination play was terrific at times and in the first 60 minutes, I thought we were excellent but once they scored, they threw caution to the wind."